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NASA NTRS2004

On the Hilbert-Huang Transform Theoretical Foundation

The Hilbert-Huang Transform [HHT] is a novel empirical method for spectrum analysis of non-linear and non-stationary signals. The HHT is a recent development and much remains to be done to establish the theoretical foundation of the HHT algorithms. This paper develops the theoretical foundation for the convergence of the HHT sifting algorithm and it proves that the finest spectrum scale will always be the first generated by the HHT Empirical Mode Decomposition (EMD) algorithm. The theoretical foundation for cutting an extrema data points set into two parts is also developed. This then allows parallel signal processing for the HHT computationally complex sifting algorithm and its optimization in hardware.

Kizhner, Semion↗

NASA NTRS1995

Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment

Collaborative optimization is a design architecture applicable in any multidisciplinary analysis environment but specifically intended for large-scale distributed analysis applications. In this approach, a complex problem is hierarchically de- composed along disciplinary boundaries into a number of subproblems which are brought into multidisciplinary agreement by a system-level coordination process. When applied to problems in a multidisciplinary design environment, this scheme has several advantages over traditional solution strategies. These advantageous features include reducing the amount of information transferred between disciplines, the removal of large iteration-loops, allowing the use of different subspace optimizers among the various analysis groups, an analysis framework which is easily parallelized and can operate on heterogenous equipment, and a structural framework that is well-suited for conventional disciplinary organizations. In this article, the collaborative architecture is developed and its mathematical foundation is presented. An example application is also presented which highlights the potential of this method for use in large-scale design applications.

Braun, R. D.↗

NASA NTRS2011

Coding for Parallel Links to Maximize the Expected Value of Decodable Messages

When multiple parallel communication links are available, it is useful to consider link-utilization strategies that provide tradeoffs between reliability and throughput. Interesting cases arise when there are three or more available links. Under the model considered, the links have known probabilities of being in working order, and each link has a known capacity. The sender has a number of messages to send to the receiver. Each message has a size and a value (i.e., a worth or priority). Messages may be divided into pieces arbitrarily, and the value of each piece is proportional to its size. The goal is to choose combinations of messages to send on the links so that the expected value of the messages decodable by the receiver is maximized. There are three parts to the innovation: (1) Applying coding to parallel links under the model; (2) Linear programming formulation for finding the optimal combinations of messages to send on the links; and (3) Algorithms for assisting in finding feasible combinations of messages, as support for the linear programming formulation. There are similarities between this innovation and methods developed in the field of network coding. However, network coding has generally been concerned with either maximizing throughput in a fixed network, or robust communication of a fixed volume of data. In contrast, under this model, the throughput is expected to vary depending on the state of the network. Examples of error-correcting codes that are useful under this model but which are not needed under previous models have been found. This model can represent either a one-shot communication attempt, or a stream of communications. Under the one-shot model, message sizes and link capacities are quantities of information (e.g., measured in bits), while under the communications stream model, message sizes and link capacities are information rates (e.g., measured in bits/second). This work has the potential to increase the value of data returned from spacecraft under certain conditions.

Klimesh, Matthew A.↗

NASA NTRS2012

Follow on Researches for X-56A Aircraft at NASA Dryden Flight Research Center (Progress Report)

A lot of composite materials are used for the modern aircraft to reduce its weight. Aircraft aeroservoelastic models are typically characterized by significant levels of model parameter uncertainty due to composite manufacturing process. Small modeling errors in the finite element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of X-56A aircraft is the flight demonstration of active flutter suppression, and therefore in this study, the identification of the primary and secondary modes is based on the flutter analysis of X-56A aircraft. It should be noted that for all three Mach number cases rigid body modes and mode numbers seven and nine are participated 89.1 92.4 % of the first flutter mode. Modal participation of the rigid body mode and mode numbers seven and nine for the second flutter mode are 94.6 96.4%. Rigid body mode and the first two anti-symmetric modes, eighth and tenth modes, are participated 93.2 94.6% of the third flutter mode. Therefore, rigid body modes and the first four flexible modes of X-56A aircraft are the primary modes during the model tuning procedure. The ground vibration test-validated structural dynamic finite element model of the X-56A aircraft is to obtain in this study. The structural dynamics finite element model of X-56A aircraft is improved using the parallelized big-bang big-crunch algorithm together with a hybrid optimization technique.

Structural Dynamic Model Tuning↗

NASA NTRS2016

Mission Analysis and Aircraft Sizing of a Hybrid-Electric Regional Aircraft

The purpose of this study was to explore advanced airframe and propulsion technologies for a small regional transport aircraft concept (approximately 50 passengers), with the goal of creating a conceptual design that delivers significant cost and performance advantages over current aircraft in that class. In turn, this could encourage airlines to open up new markets, reestablish service at smaller airports, and increase mobility and connectivity for all passengers. To meet these study goals, hybrid-electric propulsion was analyzed as the primary enabling technology. The advanced regional aircraft is analyzed with four levels of electrification, 0 percent electric with 100 percent conventional, 25 percent electric with 75 percent conventional, 50 percent electric with 50 percent conventional, and 75 percent electric with 25 percent conventional for comparison purposes. Engine models were developed to represent projected future turboprop engine performance with advanced technology and estimates of the engine weights and flowpath dimensions were developed. A low-order multi-disciplinary optimization (MDO) environment was created that could capture the unique features of parallel hybrid-electric aircraft. It is determined that at the size and range of the advanced turboprop: The battery specific energy must be 750 watt-hours per kilogram or greater for the total energy to be less than for a conventional aircraft. A hybrid vehicle would likely not be economically feasible with a battery specific energy of 500 or 750 watt-hours per kilogram based on the higher gross weight, operating empty weight, and energy costs compared to a conventional turboprop. The battery specific energy would need to reach 1000 watt-hours per kilogram by 2030 to make the electrification of its propulsion an economically feasible option. A shorter range and/or an altered propulsion-airframe integration could provide more favorable results.

Antcliff, Kevin R.↗

NASA NTRS2017

Temporal Planning for Compilation of Quantum Approximate Optimization Algorithm Circuits

We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus our initial experiments on Quantum Approximate Optimization Algorithm (QAOA) circuits that have few ordering constraints and allow highly parallel plans. We report on experiments using several temporal planners to compile circuits of various sizes to a realistic hardware. This early empirical evaluation suggests that temporal planning is a viable approach to quantum circuit compilation.

planning↗

NASA NTRSDate not supplied

Path Planning: Differential Dynamic Programming and Model Predictive Path Integral Control on VTOL Aircraft

This paper explores two optimal control approaches, widely used in robotics, to establish their viability as real-time trajectory planners for vehicle configurations envisioned for the emerging aviation sector of Urban Air Mobility (UAM). Differential Dynamic Programming (DDP) enables planning over highly nonlinear dynamics using second-order approximations along a nominal trajectory, and displays quadratic convergence to a local solution. Model Predictive Path Integral (MPPI) is a stochastic sampling-based algorithm that can optimize for general cost criteria, including potentially highly nonlinear formulations, and supports parallel computation through the use of modern GPU hardware. In this work, DDP and MPPI were implemented using model predictive control (MPC), and the results indicate they are able to successfully transition the aircraft over different flight envelopes and generate trajectories unique to UAM vehicles.

Differential Dynamic Programming↗

NASA NTRS2004

Evolutionary computing for the design search and optimization of space vehicle power subsystems

Evolutionary computing has proven to be a straightforward and robust approach for optimizing a wide range of difficult analysis and design problems. This paper discusses the application of these techniques to an existing space vehicle power subsystem resource and performance analysis simulation in a parallel processing environment.

evolutionary computing genetic algorithms optimiza↗

NASA NTRS1987

Distributed computer system enhances productivity for SRB joint optimization

Initial calculations of a redesign of the solid rocket booster joint that failed during the shuttle tragedy showed that the design had a weight penalty associated with it. Optimization techniques were to be applied to determine if there was any way to reduce the weight while keeping the joint opening closed and limiting the stresses. To allow engineers to examine as many alternatives as possible, a system was developed consisting of existing software that coupled structural analysis with optimization which would execute on a network of computer workstations. To increase turnaround, this system took advantage of the parallelism offered by the finite difference technique of computing gradients to allow several workstations to contribute to the solution of the problem simultaneously. The resulting system reduced the amount of time to complete one optimization cycle from two hours to one-half hour with a potential of reducing it to 15 minutes. The current distributed system, which contains numerous extensions, requires one hour turnaround per optimization cycle. This would take four hours for the sequential system.

Rogers, James L., Jr.↗

DOE OSTI2020

Designing a parallel Feel-the-Way clustering algorithm on HPC systems

This paper introduces a new parallel clustering algorithm, named Feel-the-Way clustering algorithm, that provides better or equivalent convergence rate than the traditional clustering methods by optimizing the synchronization and communication costs. Our algorithm design centers on how to optimize three factors simultaneously: reduced synchronizations, improved convergence rate, and retained same or comparable optimization cost. To compare the optimization cost, we use the Sum of Square Error (SSE) cost as the metric, which is the sum of the square distance between each data point and its assigned clusters. Compared with the traditional MPI k-means algorithm, the new Feel-the-Way algorithm requires less communications among participating processes. As for the convergence rate, the new algorithm requires fewer number of iterations to converge. As for the optimization cost, it obtains the SSE costs that are close to the k-means algorithm. In the paper, we first design the full-step Feel-the-Way k-means clustering algorithm that can significantly reduce the number of iterations that are required by the original k-means clustering method. Next, we improve the performance of the full-step algorithm by adopting an optimized sampling-based approach, named reassignment-history-aware sampling. Our experimental results show that the optimized sampling-based Feel-the-Way method is significantly faster than the widely used k-means clustering method, and can provide comparable optimization costs. More extensive experiments with several synthetic datasets and real-world datasets (e.g., MNIST, CIFAR-10, ENRON, and PLACES-2) show that the new parallel algorithm can outperform the open source MPI k-means library by up to 110% on a high-performance computing system using 4,096 CPU cores. In addition, the new algorithm can take up to 51% fewer iterations to converge than the k-means clustering algorithm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1980

Inventory estimation on the massively parallel processor

This paper describes algorithms for efficiently computing inventory estimates from satellite based images. The algorithms incorporate a one dimensional feature extraction which optimizes the pairwise sum of Fisher distances. Biases are eliminated with a premultiplication by the inverse of the analytically derived error matrix. The technique is demonstrated with a numerical example using statistics obtained from an actual Landsat scene. Attention was given to implementation of the Massively Parallel processor (MPP). A timing analysis demonstrates that the inventory estimation can be performed an order of magnitude faster on the MPP than on a conventional serial machine.

Argentiero, P. D.↗

NASA NTRS2017

Low-Thrust Trajectory Optimization with Simplified SQP Algorithm

The problem of low-thrust trajectory optimization in highly perturbed dynamics is a stressing case for many optimization tools. Highly nonlinear dynamics and continuous thrust are each, separately, non-trivial problems in the field of optimal control, and when combined, the problem is even more difficult. This paper de-scribes a fast, robust method to design a trajectory in the CRTBP (circular restricted three body problem), beginning with no or very little knowledge of the system. The approach is inspired by the SQP (sequential quadratic programming) algorithm, in which a general nonlinear programming problem is solved via a sequence of quadratic problems. A few key simplifications make the algorithm presented fast and robust to initial guess: a quadratic cost function, neglecting the line search step when the solution is known to be far away, judicious use of end-point constraints, and mesh refinement on multiple shooting with fixed-step integration.In comparison to the traditional approach of plugging the problem into a “black-box” NLP solver, the methods shown converge even when given no knowledge of the solution at all. It was found that the only piece of information that the user needs to provide is a rough guess for the time of flight, as the transfer time guess will dictate which set of local solutions the algorithm could converge on. This robustness to initial guess is a compelling feature, as three-body orbit transfers are challenging to design with intuition alone. Of course, if a high-quality initial guess is available, the methods shown are still valid.We have shown that endpoints can be efficiently constrained to lie on 3-body repeating orbits, and that time of flight can be optimized as well. When optimizing the endpoints, we must make a trade between converging quickly on sub-optimal endpoints or converging more slowly on end-points that are arbitrarily close to optimal. It is easy for the mission design engineer to adjust this trade based on the problem at hand.The biggest limitation to the algorithm at this point is that multi-revolution transfers (greater than 2 revolutions) do not work nearly as well. This restriction comes in because the relationship between node 1 and node N becomes increasingly nonlinear as the angular distance grows. Trans-fers with more than about 1.5 complete revolutions generally require the line search to improve convergence. Future work includes: Comparison of this algorithm with other established tools; improvements to how multiple-revolution transfers are handled; parallelization of the Jacobian computation; in-creased efficiency for the line search; and optimization of many more trajectories between a variety of 3-body orbits.

Parrish, Nathan L.↗

DOE OSTI2022

Systems and methods for tensor scheduling

A technique for efficient scheduling of operations in a program for parallelized execution thereof using a multi-processor runtime environment having two or more processors includes constraining the type or number of loop optimization transforms that may be explored such that memory and processing capacity available for the scheduling task are not exceeded, while facilitating a tradeoff between memory locality, parallelization, and/or data communication between memory modules of the multi-processor runtime environment.

Meister, Benoit J.↗

NASA NTRS1993

A fast algorithm for parallel computation of multibody dynamics on MIMD parallel architectures

In this paper the implementation of a parallel O(LogN) algorithm for computation of rigid multibody dynamics on a Hypercube MIMD parallel architecture is presented. To our knowledge, this is the first algorithm that achieves the time lower bound of O(LogN) by using an optimal number of O(N) processors. However, in addition to its theoretical significance, the algorithm is also highly efficient for practical implementation on commercially available MIMD parallel architectures due to its highly coarse grain size and simple communication and synchronization requirements. We present a multilevel parallel computation strategy for implementation of the algorithm on a Hypercube. This strategy allows the exploitation of parallelism at several computational levels as well as maximum overlapping of computation and communication to increase the performance of parallel computation.

Fijany, Amir↗

DOE OSTI2020

GronOR: Massively Parallel and GPU-Accelerated Non-Orthogonal Configuration Interaction for Large Molecular Systems

GronOR is a program package for non-orthogonal configuration interaction calculations for an electronic wave function built in terms of anti-symmetrized products of multi-configuration molecular fragment wave functions. The two-electron integrals that have to be processed may be expressed in terms of atomic orbitals or in terms of an orbital basis determined from the molecular orbitals of the fragments. The code has been specifically designed for execution on distributed memory massively parallel and Graphics Processing Unit (GPU)-accelerated computer architectures, using an MPI+OpenACC/OpenMP programming approach. The task-based execution model used in the implementation allows for linear scaling with the number of nodes on the largest pre-exascale architectures available, provides hardware fault resiliency, and enables effective execution on systems with distinct central processing unit-only and GPU-accelerated partitions. The code interfaces with existing multi-configuration electronic structure codes that provide optimized molecular fragment orbitals, configuration interaction coefficients, and the required integrals. Algorithm and implementation details, parallel and accelerated performance benchmarks, and an analysis of the sensitivity of the accuracy of results and computational performance to thresholds used in the calculations are presented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗

NASA NTRS2018

Optimization of Elastodynamic Finite Integration Technique on Intel Xeon Phi Knights Landing Processors

This work describes the development and optimization of an implementation of an isotropic elastodynamic finite integration technique (EFIT) code for parallelized computation on Intel Knights Landing (KNL) hardware. EFIT is a numerical approach resulting in standard staggered-grid finite difference equations for the elastodynamic equations of motion to simulate bulk waves is solids. The computationally efficient simulation of elastodynamic wave propagation and interactions in aerospace materials is of high-interest in the fields of nondestructive evaluation (NDE) and structural health monitoring (SHM). Ultrasonic inspection uses an ultrasonic signal, generated at the surface of the material/structure via use of a piezoelectric transducer, to propagate sound waves into the material where it interacts with any existing defects, as well as with structural boundaries and any material inhomogeneity. Reflections from defects and boundaries are then measured by a transducer. Realistic ultrasound simulation tools can significantly aid the development and optimization of inspection techniques and can assist in the interpretation of experimental data. The optimization of an elastodynamics simulation code for the KNL Many Integrated Core processor was performed. The optimization focused on data locality and vectorization. Results show that tiling of the data to exploit the cache behavior and allow for significant utilization of the KNL hardware. The MPI implementation allows for a scalable implementation enabling large problems to be simulated. The model results were validated against theoretical dispersion curves to within 2% of the group velocity, and within 0.5% of the phase velocity of the A0 mode. Aggressive use of tiling, threading, and vectorization techniques allowed for dramatically improved time to solution.

William C. Schneck↗

DOE OSTI2020

Innovative rail transport of a supersized land-based wind turbine blade

Wind turbine blade logistic providers are being challenged with escalating costs and routing complexities as one-piece blade approach lengths of 75 m in various regions of the U.S. land-based market. New lower cost solutions are needed to enable further reductions in the levelized cost of energy (LCOE) and continued market expansion. In this paper, a novel method of using existing U.S. rail infrastructure to deploy 100-m, one-piece blades to U.S. land-based wind sites is numerically investigated. The study removes the constraint that blades must be kept rigid during transport, and it allows bending to keep blades within a clearance profile while navigating horizontal and vertical curvatures. Novel system optimization and blade design processes consider blade structural constraints and rail logistic constraints in parallel to develop a highly flexible, rail-transportable blade. Results indicate maximum deployment potential in the Interior region of the United States and limited deployment potential in other regions. The study concludes that innovative rail transportation solutions combined with advanced rotor technologies can provide a feasible alternative to segmentation and support continued LCOE reductions in the U.S. land-based wind energy market.

17 WIND ENERGY↗